September 30, 2022

Numerical and Computational Challenges in Science and Engineering

Week on Computational Challenges in Mathematical Finance
February 25 - March 1, 2002

This week starts off with a two day short course on PDE methods for path dependent options , followed by a three day workshop on Computational Methods and Applications in Finance.
February 25-26
Short Course: PDE methods for Pricing Path Dependent Options
Presenters: Ken Vetzal and Peter Forsyth
**Please note attendence is limited to 25 for this course, please register early**

This course will focus on methods for pricing path dependent options using numerical PDE methods. Participants will receive detailed course notes (120 pages) and prototype Matlab software.

The course is organized so that morning sessions are lectures, while afternoons are "hands on" sessions which are devoted to using Matlab software for pricing options.

It will be assumed that the participants have a basic understanding of option pricing, and are also familiar with standard numerical algorithms, such as finite difference methods.

Schedule for both days as follows:

Morning Session to be held at The Fields Institute at 222 College Street West
8: 30 am - 9:00 am Registration and Coffee
9:00 am - 10:30 am Morning Session
10:30 am - 10:45 am Coffee Break
10:45 am - 12:00 pm Morning Session Continued
12:00 pm - 1:00 pm Lunch at The Fields Institute
Afternoon Session to be held at the Koffler Institute at 215 Huron Street, Room 208
1:00 pm - 3:00 pm Afternoon Session
3:00 pm - 3:15 pm Afternoon Tea
3:15 pm - 4:15 pm Afternoon Session Continued

An overview of the topics covered includes:

Day 1

* Introduction, comparison of PDE, Monte Carlo, Lattice methods
* Basic discretization methods
* Stability
* Causes of oscillations in Delta and Gamma
* Positive coefficent discretizations
* Smoothing discontinuous payoffs (projection, averaging)
* American options: the penalty method
* Implicit vs. explicit handling of the American constraint
* Timestep selection
* Discretely observed barriers
* Discrete non-proportional dividends

Afternoon (Matlab Sessions)
* Non-uniform grids, convergence tests
* Fully implicit vs. Crank-Nicolson
* American options: use of the Penalty method
* Variable timesteps
* Discrete Dividends
* Discontinuous Payoffs

Day 2

* Nonlinearities: uncertain volatility, transaction costs
* Convergence to the viscosity solution
* Finite volume vs. forward/backward differencing
* Path dependent options: the augmented state variable approach
* Examples: Asian options, Shouts, Parisian barriers
* Software issues: a general framework
* Implementation on high-performance architectures
* Introduction to multi-factor option pricing

Afternoon (Matlab Sessions)
* Barrier options
* Fully implicit methods for uncertain volatility models
* Asian options: interpolation effects, comparison with forward shooting grid
* Parisian options

Fee: $400 -- includes lunch and and refreshments for both days. Space in this course is limited to 25, please register early.
Please note that this course is now full.


A block of rooms for participants have been arranged the hotels listed below. Please request the Fields Institute rate when booking . Rooms must be reserved before January 22, 2002 to receive the Fields rate.

Days Inn
30 Carleton Street,
Toronto, ON, M5B 2E9
Tel: 416 977-6655
Toll Free 1-800-367-9601 (8:30 am- 6pm)
(approx. $99/night CDN)
Quality Hotel
280 Bloor Street West
Toronto, ON, M5S 1V8
Tel: (416) 968-0010
Fax: (416) 968-7765
(approx. $125/night CDN)

For additional accommodation resources, please see the Fields Housing page